Weights on all connections \(W_{ij}\)  are optimized to minimize a cost function \({E}\)  with a back propagation [1]}, i.e., \({\mathbf {w}}={\rm argmin}_{\mathbf {w}}[{E}({\mathbf {y}},{\mathcal {F}}({\mathbf {x}};{\mathbf {w}}))]\) .
In the MLP formulation, we use ReLU activation function [2]}, which works well for weight update issue of deep neural networks.
